To solve this problem, we will use the formula for freezing point depression:$\\ \Delta T_f = K_f \cdot m \\$Where:$\\$• $\Delta T_f$ is the freezing point depression.$\\$• $K_f$ is the freezing point depression constant.$\\$• $m$ is the molality of the solution.$\\$Given:$\\ K_f = 5.12 \,$K kg mol$^{-1} \\ m = 0.078 \,$mol kg$^{-1} \\$Substitute the given values into the formula:$\\ \Delta T_f = 5.12 \times 0.078 \\$Calculate $\Delta T_f: \\ \Delta T_f = 0.39936 \\$Round off $\Delta T_f$ to two decimal places:$\\ \Delta T_f = 0.40 \,$K$\\$Therefore, the freezing point depression for the solution is $0.40 \,$K$. \\$This corresponds to Option 2.